What I am hoping to be able to find is a D&D like board game that is very family friendly, and rules light. Something that still has dungeon crawling and swords and sorcery combat, but does not require the players develop any character sheets or memorize any (extensive) rule sets. Something you can just pull out of the box, set up the pieces, and start rolling dice or drawing cards.

I'm the only one in my family who's into the table top RPG thing, but I'd love to find a game that would bridge the gap that would allow me to enjoy this type of game with them, in a format they can enjoy. They are all fans of fantasy settings (Lord of the Rings, The Hobbit, etc) so that would be preferred.

Best choice is probably Betrayal at Baldur's Gate. Just because it is based on one of the best board game ever made. In general I would recommend to just get Betrayal at House on the Hill + Expansion...because it is honestly the most fun I ever had in any board game and it encourages party play/many basics of tabletop games.

There is the Vault of Dragons board game...but I can't say much about it, I didn't play it but seems to have some positive reviews.

I have to chime in with Dungeon! here. Fantastic game, has that D&D flavor, and it isn't all that complicated to learn. There are rules for advanced gameplay, such as casting spells, but for the most part the basic rules are easy to learn. Pick a token, throw some dice, and collect the treasure!

I've been loving Descent 2 for the eight year old that I'm breaking in to TTRPGs. There aren't a ton of rules, but it is similar to Hero Quest with a Game Master and players. Characters are premade but there are items and skills to pick from as you gain experience. That is optional though, since you can just set up an encounter and play too.